An Improved Forecast of Patchy Reionization Reconstruction with CMB

Inhomogeneous reionization gives rise to angular fluctuations in the Cosmic Microwave Background (CMB) optical depth tau(n) to the last scattering surface, correlating different spherical harmonic modes and imprinting characteristic non-Gaussianity on CMB maps. Recently the minimum variance quadratic estimator has been derived using this mode-coupling signal, and found that the optical depth fluctuations could be detected with (S/N)^2 ~ 100 in futuristic experiments like CMBPol. We first demonstrate that the non-Gaussian signal from gravitational lensing of CMB is the dominant source of contamination for reconstructing inhomogeneous reionization signals, even with 98% of its contribution removed by delensing. We then construct unbiased estimators that simultaneously reconstruct inhomogeneous reionization signals tau(n) and gravitational lensing potential phi(n). We apply our new unbiased estimators to future CMB experiment to assess the detectability of inhomogeneous reionization signals. With more physically motivated simulations of inhomogenuous reionizations that predict an order of magnitude smaller optical depth power spectrum than previous studies, we show that a CMBPol-like experiment could achieve a marginal detection of inhomogeneous reionization,(S/N)^2 ~ O(1) with this quadratic estimator to ~O(10) with the analogous maximum likelihood estimator.